A damping device of this kind having an armature, which is designed as a disk-shaped rotor and which has an annular disk-shaped armature part of aluminum, is known in the field. The armature part is mounted on a rotating shaft which, under certain operating conditions, exhibits speed fluctuations caused by spurious oscillations. In response to the occurrence of such speed fluctuations, a direct current is fed with the aid of a control device into a winding of the exciter in order to induce a magnetic flux in a soft magnetic core of the exciter that permeates a partial region of the armature part which is radially spaced apart from the shaft's axis of rotation and is located between the teeth of the soft magnetic core. In this context, the direction of rotation of the armature part is oriented transversely to the magnetic flux that permeates it, so that electric currents are induced in the partial region of the armature part permeated by the magnetic flux. These electric currents produce heat losses in the armature part which damp the spurious oscillations. The damping device still has the disadvantage, however, of having sizable dimensions and only a relatively negligible damping moment. Therefore, for all intents and purposes, the damping device is not well suited for damping spurious oscillations occurring on the drive shaft of an automotive combustion engine.